I. Field of the Invention
The present invention relates to a method of designing control laws (e.g., flight control laws in an airplane) by applying a technique called Multi-Input, Multi-Output (MIMO) feedback LTI""zation, which is applicable to solving a feedback control design problem for a class of nonlinear and linear parameter dependent (xe2x80x9cLPDxe2x80x9d) dynamic systems, also known as linear parameter varying (xe2x80x9cLPVxe2x80x9d), with multiple inputs and multiple outputs. Feedback LTI""zation combines a co-ordinates transformation and a feedback control law, the results of which cancel system parameter dependent terms and yield the transformed space open loop system linear time invariant (LTI). The present invention further relates to using multi-input feedback LTI""zation to solve the control design problem associated with control systems for LPD dynamic devices. In particular, the invention is applied to a feedback control system for controlling a parameter dependent dynamic device (e.g., an airplane) with multiple control inputs.
II. Background
Design techniques used for solving feedback control design problems can be divided into several classes. For example, two broad classes are (1) Linear Time Invariant systems (herein after referred to as xe2x80x9cLTIxe2x80x9d) and (2) nonlinear systems. In the last four decades, LTI systems have received a great deal of attention resulting in many well-defined control design techniques. See, e.g., Maciejowski, J. M., Multivariable Feedback Design, 1989, Addison-Wesley and Reid, J. G., Linear System Fundamentals, 1983, McGraw-Hill, each incorporated herein by reference. Nonlinear systems have, in contrast, received far less attention. Consequently, a smaller set of techniques has been developed for use in feedback control system design for nonlinear systems or linear parameter dependent systems. As a result, control law design for nonlinear systems can be an arduous task. Typically, control laws consist of a plurality of equations used to control a dynamic device in a desirable and predictable manner. Previously, designing control laws for LPD systems using quasi-static LTI design techniques could require an enormous amount of effort, often entailing weeks, if not months, of time to complete a single full envelope design. For example, when designing a flight control law, designers must predict and then design the control law to accommodate a multitude (often thousands) of operating points within the flight envelope (i.e., the operating or performance limits for an aircraft).
Feedback Linearization (reference may be had to Isidori, A., Nonlinear Control Systems, 2nd Edition, 1989, Springer-Verlag, herein incorporated by reference), is applicable to control design for a broad class of nonlinear systems, but does not explicitly accommodate system parameter changes at arbitrary rates. Feedback LTI""zation, a technique used for rendering a control system model linear time invariant, for single input systems is outlined in the Ph.D. thesis of the inventor, Dr. David W. Vos, xe2x80x9cNon-linear Control Of An Autonomous Unicycle Robot; Practical Issues,xe2x80x9d Massachusetts Institute of Technology, 1992, incorporated herein by reference. This thesis extends Feedback Linearization to explicitly accommodate fast parameter variations. However, the Ph.D. thesis does not give generally applicable solutions or algorithms for applying feedback LTI""zation to either single input or multi-input parameter dependent dynamic systems. U.S. Pat. No. 5,615,119 (herein incorporated by reference, and hereafter the xe2x80x9c""119xe2x80x9d patent) addressed this problem, albeit in the context of failure detection filter design. In particular, the ""119 patent describes a fault tolerant control system including (i) a coordinate transforming diffeomorphism and (ii) a feedback control law, which produces a control system model that is linear time invariant (a feedback control law which renders a control system model linear time invariant is hereinafter termed xe2x80x9ca feedback LTI""ing control lawxe2x80x9d).
The ""119 patent encompasses fault detection and isolation and control law reconfiguration by transforming various actuator and sensor signals into a linear time invariant coordinate system within which an LTI failure detection filter can be executed, to thus provide a capability for failure detection and isolation for dynamic systems whose parameters vary over time. That is, a detection filter may be implemented in a so-called Z-space in which the system may be represented as linear time invariant and is independent of the dynamic system parameters.
What is needed, however, is the further extension of the feedback LTIzation control law principals in the ""119 patent to multi-input parameter dependent systems. Furthermore, control system designers have long experienced a need for a fast and efficient method of designing control laws relating to parameter dependent nonlinear systems. An efficient method of control law design is therefore needed. Similarly, there is also a need for a control system aimed at controlling such a dynamic device with multiple control inputs.
The present invention specifically solves a Multi-Input feedback LTI""zation problem, and shows a method for feedback control law design for a parameter dependent dynamic device (e.g., an airplane) class of systems. Additionally, the present invention provides a control system for controlling a parameter dependent dynamic device with multiple inputs. The present invention is also applicable to the methods and systems discussed in the above-mentioned ""119 patent (i.e., for failure detection system design in the multi-input case). As a result of the concepts of this invention, control system designers may now shave weeks or months off of their design time.
According to one aspect of the invention, an automatic control system for controlling a dynamic device is provided. The device includes sensors and control laws stored in a memory. The control system includes a receiving means for receiving status signals (measuring the state vector) and current external condition signals (measuring parameter values) from the sensors, and for receiving reference signals. Also included is processing structure for: (i) selecting and applying gain schedules to update the control laws, wherein the gain schedules correspond to the current external conditions signals (parameter values) and are generated in a multi-input linear time invariant coordinates system; (ii) determining parameter rates of change and applying the parameter rates of change to update the control laws; (iii) applying device status signal feedback to update the control laws; and (iv) controlling the device based on the updated control laws.
According to another aspect of the invention, a method for designing flight control laws using multi-input parameter dependent feedback is provided. The method includes the following steps: (i) determining a coordinates system for flight vehicle equations of motion; (ii) transforming the coordinates system for the flight vehicle equations of motion into a multi-input linear time invariant system; (iii) establishing control criteria yielding the transformed coordinates equations of motion LTI; (iv) adjusting the control criteria to obtain a desired closed loop behavior for the controlled system; and (v) converting the transformed coordinates control laws to physical coordinates.
According to still another aspect of the invention, a method of controlling a dynamic device is provided. The device including actuators, sensors and control laws stored in a memory. The method includes the following steps: (i) transforming device characteristics into a multi-input linear time invariant system; (ii) selecting and applying physical gain schedules to the control laws, the gain schedules corresponding to the current external condition signals; (iii) determining and applying parameter rates of change to update the control laws; (iv) applying device status signal feedback to update the control laws; (v) converting the transformed coordinates control laws to physical coordinates; and (vi) controlling the device based on the updated control laws.
Specific computer executable software stored on a computer or processor readable medium is also another aspect of the present invention. This software code for developing control laws for dynamic devices includes: (i) code to transform device characteristics into a multi-input linear time invariant system; (ii) code to establish control criteria yielding the transformed coordinates equations of motion LTI; (iii) code to define a design point in the multi-input linear time invariant system; (iv) code to adjust the transformations to correspond with the design point; and (v) code to develop a physical coordinates control law corresponding to the adjusted transformations; and (vi) code to apply reverse transformations to cover the full design envelope.
In yet another aspect of the present invention, a multi-input parameter dependent control system for controlling an aircraft is provided. The system includes receiving means for receiving aircraft status signals and for receiving current external condition signals. A memory having at least one region for storing computer executable code is also included. A processor for executing the program code is provided, wherein the program code includes code to: (i) transform the aircraft characteristics into a multi-input linear time invariant system; (ii) select and apply gain schedules to flight control laws, the gain schedules corresponding to the current external condition signals; (iii) determine parameter rates of change, and to apply the parameter rates of change to the flight control laws; (iv) apply feedback from the aircraft status signals to the flight control laws; (v) convert the transformed coordinates control laws to physical coordinates; and (vi) control the aircraft based on the updated flight control laws.